Variational regularization of damage models based on the emulated RVE

authored by: S. Schwarz, Philipp Junker, K. Hackl
Abstract: Material models exhibiting softening effects due to damage or localization share the problem of leading to ill-posed boundary value problems that lead to physically meaningless, mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior, described, e.g., by internal variables, at a spatial level. The common way to do this is to take into account higher gradients of the field variables, thus introducing an internal length scale. In this paper, we suggest a different approach to regularization that does not make use of any nonlocal enhancement like the inclusion of higher gradients or integration over local sub-domains nor of any classical viscous effects. Instead we perform an appropriate relaxation of the (condensed) free energy in a time-incremental setting which leads to a modified energy that is coercive and satisfies quasiconvexity in an approximate way. Thus, in every time increment a regular boundary value problem is solved. The proposed approach holds the same advantage as other methods, but with less numerical effort. We start with the theoretical derivation, discuss a rate-independent version of the proposed model and present details of the numerical treatment. Finally, we give finite element results that demonstrate the efficiency of this new approach.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Continuum Mechanics and Thermodynamics
Volume: 33
Pages: 69-95
No. of pages: 27
ISSN: 0935-1175
Publication date: 01.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: General Materials Science, Mechanics of Materials, General Physics and Astronomy
Electronic version(s): https://doi.org/10.1007/s00161-020-00886-0 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{d40718c89756488281da618c62261743,
title = "Variational regularization of damage models based on the emulated RVE",
abstract = "Material models exhibiting softening effects due to damage or localization share the problem of leading to ill-posed boundary value problems that lead to physically meaningless, mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior, described, e.g., by internal variables, at a spatial level. The common way to do this is to take into account higher gradients of the field variables, thus introducing an internal length scale. In this paper, we suggest a different approach to regularization that does not make use of any nonlocal enhancement like the inclusion of higher gradients or integration over local sub-domains nor of any classical viscous effects. Instead we perform an appropriate relaxation of the (condensed) free energy in a time-incremental setting which leads to a modified energy that is coercive and satisfies quasiconvexity in an approximate way. Thus, in every time increment a regular boundary value problem is solved. The proposed approach holds the same advantage as other methods, but with less numerical effort. We start with the theoretical derivation, discuss a rate-independent version of the proposed model and present details of the numerical treatment. Finally, we give finite element results that demonstrate the efficiency of this new approach.",
keywords = "Damage, Quasiconvex envelope, Relaxation, Variational methods",
author = "S. Schwarz and Philipp Junker and K. Hackl",
year = "2021",
month = jan,
doi = "10.1007/s00161-020-00886-0",
language = "English",
volume = "33",
pages = "69--95",
journal = "Continuum Mechanics and Thermodynamics",
issn = "0935-1175",
publisher = "Springer New York",
number = "1",
}